LPP

Let the company produce x type A and y type B belts

 

Also, let the time taken to make type B belts be m hours and hence, the time taken to make type A belt would be 2m hours

 

The total time to make these belts  = 2mx + ym

 

Since, at max the company can make at the most 1000 type B belts per day

 

Hence, in any given day, 2mx+ym <= 1000m

2x+y <= 1000  (1)

 

Also, x<=400 (2) and y<=700 (3)

 

Also, x+y<=800 (4) 

 

Also, x>=0 and y>=0

 

Profit = 2x+1.5y 

We need to maximise profit given the constraints. So, for that draw all the 6 lines on the graph and check the common area, you will form a hexagon ABCDEF with A(0,700); B(100,700); C(200,600); D(400,200); E(400,0); F(0,0)

 

Since the feasible region is a bound region, we can check the profit function at all the vertices to find the point of maxima

 

At point A: 2(0)+1.5(700) = 1050

At point B: 2(100)+1.5(700) = 1250

At point C: 2(200)+1.5(600) = 1300

At point D: 2(400)+1.5(200) = 1100

At point E: 2(400)+1.5(0) = 800

At point F: 2(0)+1.5(0) = 0

 

So, the maxima lies at point C with x = 200 and y = 600 and the maximum profit = Rs 1300.